Network curvature as a hallmark of brain structural connectivity

Curvature-enhanced graph convolutional network for biomolecular interaction prediction

Geometric deep learning has demonstrated a great potential in non-Euclidean data analysis. The incorporation of geometric insights into learning architecture is vital to its success. Here we propose a curvature-enhanced graph convolutional network (CGCN) for biomolecular interaction prediction. Our CGCN employs Ollivier-Ricci curvature (ORC) to characterize network local geometric properties and enhance the learning capability of GCNs. More specifically, ORCs are evaluated based on the local topology from node neighborhoods, and further incorporated into the weight function for the feature aggregation in message-passing procedure. Our CGCN model is extensively validated on fourteen real-world bimolecular interaction networks and analyzed in details using a series of well-designed simulated data. It has been found that our CGCN can achieve the state-of-the-art results. It outperforms all existing models, as far as we know, in thirteen out of the fourteen real-world datasets and ranks as the second in the rest one. The results from the simulated data show that our CGCN model is superior to the traditional GCN models regardless of the positive-to-negative-curvature ratios, network densities, and network sizes (when larger than 500).

Structural Brain Connectivity and Treatment Improvement in Mood Disorder

Background: The treatment of depressive episodes is well established, with clearly demonstrated effectiveness of antidepressants and psychotherapies. However, more than one-third of depressed patients do not respond to treatment. Identifying the brain structural basis of treatment-resistant depression could prevent useless pharmacological prescriptions, adverse events, and lost therapeutic opportunities. Methods: Using diffusion magnetic resonance imaging, we performed structural connectivity analyses on a cohort of 154 patients with mood disorder (MD) and 77 sex- and age-matched healthy control (HC) participants. To assess illness improvement, the patients with MD went through two clinical interviews at baseline and at 6-month follow-up and were classified based on the Clinical Global Impression-Improvement score into improved or not-improved (NI). First, the threshold-free network-based statistics (NBS) was conducted to measure the differences in regional network architecture. Second, nonparametric permutations tests were performed on topological metrics based on graph theory to examine differences in connectome organization. Results: The threshold-free NBS revealed impaired connections involving regions of the basal ganglia in patients with MD compared with HC. Significant increase of local efficiency and clustering coefficient was found in the lingual gyrus, insula, and amygdala in the MD group. Compared with the NI, the improved displayed significantly reduced network integration and segregation, predominately in the default-mode regions, including the precuneus, middle temporal lobe, and rostral anterior cingulate. Conclusions: This study highlights the involvement of regions belonging to the basal ganglia, the fronto-limbic network, and the default mode network, leading to a better understanding of MD disease and its unfavorable outcome.

Does the brain behave like a (complex) network? I. Dynamics

Graph theory is now becoming a standard tool in system-level neuroscience. However, endowing observed brain anatomy and dynamics with a complex network structure does not entail that the brain actually works as a network. Asking whether the brain behaves as a network means asking whether network properties count. From the viewpoint of neurophysiology and, possibly, of brain physics, the most substantial issues a network structure may be instrumental in addressing relate to the influence of network properties on brain dynamics and to whether these properties ultimately explain some aspects of brain function. Here, we address the dynamical implications of complex network, examining which aspects and scales of brain activity may be understood to genuinely behave as a network. To do so, we first define the meaning of networkness, and analyse some of its implications. We then examine ways in which brain anatomy and dynamics can be endowed with a network structure and discuss possible ways in which network structure may be shown to represent a genuine organisational principle of brain activity, rather than just a convenient description of its anatomy and dynamics.

EXO1/P53/SREBP1 axis-regulated lipid metabolism promotes prostate cancer progression

Prostate cancer (PCa) is one of the most common malignant tumors affecting the male genitourinary system. However, there is currently a lack of effective treatments for patients with advanced prostate cancer, which significantly impacts men's overall health. Exonuclease 1 (EXO1), a protein with mismatch repair and recombination functions, has been found to play a vital role in various diseases. In our study, we discovered that EXO1 acts as a novel biomarker of PCa, which promotes prostate cancer progression by regulating lipid metabolism reprogramming in prostate cancer cells. Mechanistically, EXO1 promotes the expression of SREBP1 by inhibiting the P53 signaling pathway. In summary, our findings suggest that EXO1 regulated intracellular lipid reprogramming through the P53/SREBP1 axis, thus promoting PCa progression. The result could potentially lead to new insights and therapeutic targets for diagnosing and treating PCa.

Dynamic network curvature analysis of gene expression reveals novel potential therapeutic targets in sarcoma

Network properties account for the complex relationship between genes, making it easier to identify complex patterns in their interactions. In this work, we leveraged these network properties for dual purposes. First, we clustered pediatric sarcoma tumors using network information flow as a similarity metric, computed by the Wasserstein distance. We demonstrate that this approach yields the best concordance with histological subtypes, validated against three state-of-the-art methods. Second, to identify molecular targets that would be missed by more conventional methods of analysis, we applied a novel unsupervised method to cluster gene interactomes represented as networks in pediatric sarcoma. RNA-Seq data were mapped to protein-level interactomes to construct weighted networks that were then subjected to a non-Euclidean, multi-scale geometric approach centered on a discrete notion of curvature. This provides a measure of the functional association among genes in the context of their connectivity. In confirmation of the validity of this method, hierarchical clustering revealed the characteristic EWSR1-FLI1 fusion in Ewing sarcoma. Furthermore, assessing the effects of in silico edge perturbations and simulated gene knockouts as quantified by changes in curvature, we found non-trivial gene associations not previously identified.

DomiRank Centrality reveals structural fragility of complex networks via node dominance

Determining the key elements of interconnected infrastructure and complex systems is paramount to ensure system functionality and integrity. This work quantifies the dominance of the networks' nodes in their respective neighborhoods, introducing a centrality metric, DomiRank, that integrates local and global topological information via a tunable parameter. We present an analytical formula and an efficient parallelizable algorithm for DomiRank centrality, making it applicable to massive networks. From the networks' structure and function perspective, nodes with high values of DomiRank highlight fragile neighborhoods whose integrity and functionality are highly dependent on those dominant nodes. Underscoring this relation between dominance and fragility, we show that DomiRank systematically outperforms other centrality metrics in generating targeted attacks that effectively compromise network structure and disrupt its functionality for synthetic and real-world topologies. Moreover, we show that DomiRank-based attacks inflict more enduring damage in the network, hindering its ability to rebound and, thus, impairing system resilience. DomiRank centrality capitalizes on the competition mechanism embedded in its definition to expose the fragility of networks, paving the way to design strategies to mitigate vulnerability and enhance the resilience of critical infrastructures.

Discrete Ricci curvatures capture age-related changes in human brain functional connectivity networks

Introduction

Geometry-inspired notions of discrete Ricci curvature have been successfully used as markers of disrupted brain connectivity in neuropsychiatric disorders, but their ability to characterize age-related changes in functional connectivity is unexplored.

Methods

We apply Forman-Ricci curvature and Ollivier-Ricci curvature to compare functional connectivity networks of healthy young and older subjects from the Max Planck Institute Leipzig Study for Mind-Body-Emotion Interactions (MPI-LEMON) dataset (N = 225).

Results

We found that both Forman-Ricci curvature and Ollivier-Ricci curvature can capture whole-brain and region-level age-related differences in functional connectivity. Meta-analysis decoding demonstrated that those brain regions with age-related curvature differences were associated with cognitive domains known to manifest age-related changes-movement, affective processing, and somatosensory processing. Moreover, the curvature values of some brain regions showing age-related differences exhibited correlations with behavioral scores of affective processing. Finally, we found an overlap between brain regions showing age-related curvature differences and those brain regions whose non-invasive stimulation resulted in improved movement performance in older adults.

Discussion

Our results suggest that both Forman-Ricci curvature and Ollivier-Ricci curvature correctly identify brain regions that are known to be functionally or clinically relevant. Our results add to a growing body of evidence demonstrating the sensitivity of discrete Ricci curvature measures to changes in the organization of functional connectivity networks, both in health and disease.

Statistical power in network neuroscience

Network neuroscience has emerged as a leading method to study brain connectivity. The success of these investigations is dependent not only on approaches to accurately map connectivity but also on the ability to detect real effects in the data - that is, statistical power. We review the state of statistical power in the field and discuss sample size, effect size, measurement error, and network topology as key factors that influence the power of brain connectivity investigations. We use the term 'differential power' to describe how power can vary between nodes, edges, and graph metrics, leaving traces in both positive and negative connectome findings. We conclude with strategies for working with, rather than around, power in connectivity studies.

Changes in the geometry and robustness of diffusion tensor imaging networks: Secondary analysis from a randomized controlled trial of young autistic children receiving an umbilical cord blood infusion

Diffusion tensor imaging (DTI) has been used as an outcome measure in clinical trials for several psychiatric disorders but has rarely been explored in autism clinical trials. This is despite a large body of research suggesting altered white matter structure in autistic individuals. The current study is a secondary analysis of changes in white matter connectivity from a double-blind placebo-control trial of a single intravenous cord blood infusion in 2-7-year-old autistic children (1). Both clinical assessments and DTI were collected at baseline and 6 months after infusion. This study used two measures of white matter connectivity: change in node-to-node connectivity as measured through DTI streamlines and a novel measure of feedback network connectivity, Ollivier-Ricci curvature (ORC). ORC is a network measure which considers both local and global connectivity to assess the robustness of any given pathway. Using both the streamline and ORC analyses, we found reorganization of white matter pathways in predominantly frontal and temporal brain networks in autistic children who received umbilical cord blood treatment versus those who received a placebo. By looking at changes in network robustness, this study examined not only the direct, physical changes in connectivity, but changes with respect to the whole brain network. Together, these results suggest the use of DTI and ORC should be further explored as a potential biomarker in future autism clinical trials. These results, however, should not be interpreted as evidence for the efficacy of cord blood for improving clinical outcomes in autism. This paper presents a secondary analysis using data from a clinical trial that was prospectively registered with ClinicalTrials.gov(NCT02847182).

The network collapse in multiple sclerosis: An overview of novel concepts to address disease dynamics

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Multiple sclerosis (MS) can be considered as a network disorder.

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This review discusses network concepts in order to understand progression in MS.

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Damage is hypothesized to lead to a “network collapse” and clinical progression.

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New concepts are discussed that will likely influence the field in the near future.

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These include brain wiring, how regions communicate and robustness to damage.

Multiple sclerosis is a neuroinflammatory and neurodegenerative disorder of the central nervous system that can be considered a network disorder. In MS, lesional pathology continuously disconnects structural pathways in the brain, forming a disconnection syndrome. Complex functional network changes then occur that are poorly understood but closely follow clinical status. Studying these structural and functional network changes has been and remains crucial to further decipher complex symptoms like cognitive impairment and physical disability. Recent insights especially implicate the importance of monitoring network hubs in MS, like the thalamus and default-mode network which seem especially hit hard. Such network insights in MS have led to the hypothesis that as the network continues to become disconnected and dysfunctional, exceeding a certain threshold of network efficiency loss leads to a “network collapse”. After this collapse, crucial network hubs become rigid and overloaded, and at the same time a faster neurodegeneration and accelerated clinical (and cognitive) progression can be seen. As network neuroscience has evolved, the MS field can now move towards a clearer classification of the network collapse itself and specific milestone events leading up to it. Such an updated network-focused conceptual framework of MS could directly impact clinical decision making as well as the design of network-tailored rehabilitation strategies. This review therefore provides an overview of recent network concepts that have enhanced our understanding of clinical progression in MS, especially focusing on cognition, as well as new concepts that will likely move the field forward in the near future.

Inferring functional communities from partially observed biological networks exploiting geometric topology and side information

Cellular biological networks represent the molecular interactions that shape function of living cells. Uncovering the organization of a biological network requires efficient and accurate algorithms to determine the components, termed communities, underlying specific processes. Detecting functional communities is challenging because reconstructed biological networks are always incomplete due to technical bias and biological complexity, and the evaluation of putative communities is further complicated by a lack of known ground truth. To address these challenges, we developed a geometric-based detection framework based on Ollivier-Ricci curvature to exploit information about network topology to perform community detection from partially observed biological networks. We further improved this approach by integrating knowledge of gene function, termed side information, into the Ollivier-Ricci curvature algorithm to aid in community detection. This approach identified essential conserved and varied biological communities from partially observed Arabidopsis protein interaction datasets better than the previously used methods. We show that Ollivier-Ricci curvature with side information identified an expanded auxin community to include an important protein stability complex, the Cop9 signalosome, consistent with previous reported links to auxin response and root development. The results show that community detection based on Ollivier-Ricci curvature with side information can uncover novel components and novel communities in biological networks, providing novel insight into the organization and function of complex networks.

Graph Ricci curvatures reveal atypical functional connectivity in autism spectrum disorder

While standard graph-theoretic measures have been widely used to characterize atypical resting-state functional connectivity in autism spectrum disorder (ASD), geometry-inspired network measures have not been applied. In this study, we apply Forman–Ricci and Ollivier–Ricci curvatures to compare networks of ASD and typically developing individuals (N = 1112) from the Autism Brain Imaging Data Exchange I (ABIDE-I) dataset. We find brain-wide and region-specific ASD-related differences for both Forman–Ricci and Ollivier–Ricci curvatures, with region-specific differences concentrated in Default Mode, Somatomotor and Ventral Attention networks for Forman–Ricci curvature. We use meta-analysis decoding to demonstrate that brain regions with curvature differences are associated to those cognitive domains known to be impaired in ASD. Further, we show that brain regions with curvature differences overlap with those brain regions whose non-invasive stimulation improves ASD-related symptoms. These results suggest the utility of graph Ricci curvatures in characterizing atypical connectivity of clinically relevant regions in ASD and other neurodevelopmental disorders.

Mapping the Human Connectome using Diffusion MRI at 300 mT/m Gradient Strength: Methodological Advances and Scientific Impact

Tremendous efforts have been made in the last decade to advance cutting-edge MRI technology in pursuit of mapping structural connectivity in the living human brain with unprecedented sensitivity and speed. The first Connectom 3T MRI scanner equipped with a 300 mT/m whole-body gradient system was installed at the Massachusetts General Hospital in 2011 and was specifically constructed as part of the Human Connectome Project. Since that time, numerous technological advances have been made to enable the broader use of the Connectom high gradient system for diffusion tractography and tissue microstructure studies and leverage its unique advantages and sensitivity to resolving macroscopic and microscopic structural information in neural tissue for clinical and neuroscientific studies. The goal of this review article is to summarize the technical developments that have emerged in the last decade to support and promote large-scale and scientific studies of the human brain using the Connectom scanner. We provide a brief historical perspective on the development of Connectom gradient technology and the efforts that led to the installation of three other Connectom 3T MRI scanners worldwide - one in the United Kingdom in Cardiff, Wales, another in Continental Europe in Leipzig, Germany, and the latest in Asia in Shanghai, China. We summarize the key developments in gradient hardware and image acquisition technology that have formed the backbone of Connectom-related research efforts, including the rich array of high-sensitivity receiver coils, pulse sequences, image artifact correction strategies and data preprocessing methods needed to optimize the quality of high-gradient strength dMRI data for subsequent analyses. Finally, we review the scientific impact of the Connectom MRI scanner, including advances in diffusion tractography, tissue microstructural imaging, ex vivo validation, and clinical investigations that have been enabled by Connectom technology. We conclude with brief insights into the unique value of strong gradients for dMRI and where the field is headed in the coming years.

A hands-on tutorial on network and topological neuroscience

The brain is an extraordinarily complex system that facilitates the optimal integration of information from different regions to execute its functions. With the recent advances in technology, researchers can now collect enormous amounts of data from the brain using neuroimaging at different scales and from numerous modalities. With that comes the need for sophisticated tools for analysis. The field of network neuroscience has been trying to tackle these challenges, and graph theory has been one of its essential branches through the investigation of brain networks. Recently, topological data analysis has gained more attention as an alternative framework by providing a set of metrics that go beyond pairwise connections and offer improved robustness against noise. In this hands-on tutorial, our goal is to provide the computational tools to explore neuroimaging data using these frameworks and to facilitate their accessibility, data visualisation, and comprehension for newcomers to the field. We will start by giving a concise (and by no means complete) overview of the field to introduce the two frameworks and then explain how to compute both well-established and newer metrics on resting-state functional magnetic resonance imaging. We use an open-source language (Python) and provide an accompanying publicly available Jupyter Notebook that uses the 1000 Functional Connectomes Project dataset. Moreover, we would like to highlight one part of our notebook dedicated to the realistic visualisation of high order interactions in brain networks. This pipeline provides three-dimensional (3-D) plots of pairwise and higher-order interactions projected in a brain atlas, a new feature tailor-made for network neuroscience.

Comprehensive diffusion MRI dataset for in vivo human brain microstructure mapping using 300 mT/m gradients

Strong gradient systems can improve the signal-to-noise ratio of diffusion MRI measurements and enable a wider range of acquisition parameters that are beneficial for microstructural imaging. We present a comprehensive diffusion MRI dataset of 26 healthy participants acquired on the MGH-USC 3 T Connectome scanner equipped with 300 mT/m maximum gradient strength and a custom-built 64-channel head coil. For each participant, the one-hour long acquisition systematically sampled the accessible diffusion measurement space, including two diffusion times (19 and 49 ms), eight gradient strengths linearly spaced between 30 mT/m and 290 mT/m for each diffusion time, and 32 or 64 uniformly distributed directions. The diffusion MRI data were preprocessed to correct for gradient nonlinearity, eddy currents, and susceptibility induced distortions. In addition, scan/rescan data from a subset of seven individuals were also acquired and provided. The MGH Connectome Diffusion Microstructure Dataset (CDMD) may serve as a test bed for the development of new data analysis methods, such as fiber orientation estimation, tractography and microstructural modelling.

The Role of Diffusion Tensor MR Imaging (DTI) of the Brain in Diagnosing Autism Spectrum Disorder: Promising Results

Autism spectrum disorder (ASD) is a combination of developmental anomalies that causes social and behavioral impairments, affecting around 2% of US children. Common symptoms include difficulties in communications, interactions, and behavioral disabilities. The onset of symptoms can start in early childhood, yet repeated visits to a pediatric specialist are needed before reaching a diagnosis. Still, this diagnosis is usually subjective, and scores can vary from one specialist to another. Previous literature suggests differences in brain development, environmental, and/or genetic factors play a role in developing autism, yet scientists still do not know exactly the pathology of this disorder. Currently, the gold standard diagnosis of ASD is a set of diagnostic evaluations, such as the Autism Diagnostic Observation Schedule (ADOS) or Autism Diagnostic Interview-Revised (ADI-R) report. These gold standard diagnostic instruments are an intensive, lengthy, and subjective process that involves a set of behavioral and communications tests and clinical history information conducted by a team of qualified clinicians. Emerging advancements in neuroimaging and machine learning techniques can provide a fast and objective alternative to conventional repetitive observational assessments. This paper provides a thorough study of implementing feature engineering tools to find discriminant insights from brain imaging of white matter connectivity and using a machine learning framework for an accurate classification of autistic individuals. This work highlights important findings of impacted brain areas that contribute to an autism diagnosis and presents promising accuracy results. We verified our proposed framework on a large publicly available DTI dataset of 225 subjects from the Autism Brain Imaging Data Exchange-II (ABIDE-II) initiative, achieving a high global balanced accuracy over the 5 sites of up to 99% with 5-fold cross validation. The data used was slightly unbalanced, including 125 autistic subjects and 100 typically developed (TD) ones. The achieved balanced accuracy of the proposed technique is the highest in the literature, which elucidates the importance of feature engineering steps involved in extracting useful knowledge and the promising potentials of adopting neuroimaging for the diagnosis of autism.

Geometric network analysis provides prognostic information in patients with high grade serous carcinoma of the ovary treated with immune checkpoint inhibitors

Network analysis methods can potentially quantify cancer aberrations in gene networks without introducing fitted parameters or variable selection. A new network curvature-based method is introduced to provide an integrated measure of variability within cancer gene networks. The method is applied to high-grade serous ovarian cancers (HGSOCs) to predict response to immune checkpoint inhibitors (ICIs) and to rank key genes associated with prognosis. Copy number alterations (CNAs) from targeted and whole-exome sequencing data were extracted for HGSOC patients (n = 45) treated with ICIs. CNAs at a gene level were represented on a protein–protein interaction network to define patient-specific networks with a fixed topology. A version of Ollivier–Ricci curvature was used to identify genes that play a potentially key role in response to immunotherapy and further to stratify patients at high risk of mortality. Overall survival (OS) was defined as the time from the start of ICI treatment to either death or last follow-up. Kaplan–Meier analysis with log-rank test was performed to assess OS between the high and low curvature classified groups. The network curvature analysis stratified patients at high risk of mortality with p = 0.00047 in Kaplan–Meier analysis in HGSOC patients receiving ICI. Genes with high curvature were in accordance with CNAs relevant to ovarian cancer. Network curvature using CNAs has the potential to be a novel predictor for OS in HGSOC patients treated with immunotherapy.

Understanding Changes in the Topology and Geometry of Financial Market Correlations during a Market Crash

In econophysics, the achievements of information filtering methods over the past 20 years, such as the minimal spanning tree (MST) by Mantegna and the planar maximally filtered graph (PMFG) by Tumminello et al., should be celebrated. Here, we show how one can systematically improve upon this paradigm along two separate directions. First, we used topological data analysis (TDA) to extend the notions of nodes and links in networks to faces, tetrahedrons, or k-simplices in simplicial complexes. Second, we used the Ollivier-Ricci curvature (ORC) to acquire geometric information that cannot be provided by simple information filtering. In this sense, MSTs and PMFGs are but first steps to revealing the topological backbones of financial networks. This is something that TDA can elucidate more fully, following which the ORC can help us flesh out the geometry of financial networks. We applied these two approaches to a recent stock market crash in Taiwan and found that, beyond fusions and fissions, other non-fusion/fission processes such as cavitation, annihilation, rupture, healing, and puncture might also be important. We also successfully identified neck regions that emerged during the crash, based on their negative ORCs, and performed a case study on one such neck region.

Unfolding the multiscale structure of networks with dynamical Ollivier-Ricci curvature

Describing networks geometrically through low-dimensional latent metric spaces has helped design efficient learning algorithms, unveil network symmetries and study dynamical network processes. However, latent space embeddings are limited to specific classes of networks because incompatible metric spaces generally result in information loss. Here, we study arbitrary networks geometrically by defining a dynamic edge curvature measuring the similarity between pairs of dynamical network processes seeded at nearby nodes. We show that the evolution of the curvature distribution exhibits gaps at characteristic timescales indicating bottleneck-edges that limit information spreading. Importantly, curvature gaps are robust to large fluctuations in node degrees, encoding communities until the phase transition of detectability, where spectral and node-clustering methods fail. Using this insight, we derive geometric modularity to find multiscale communities based on deviations from constant network curvature in generative and real-world networks, significantly outperforming most previous methods. Our work suggests using network geometry for studying and controlling the structure of and information spreading on networks.

The relationships between the topological properties of the whole-brain white matter network and the severity of autism spectrum disorder: A study from monozygotic twins

Twins provide a valuable perspective for exploring the pathological mechanism of autism spectrum disorder (ASD). We aim to analyze differences in the topological properties of the white matter (WM) network between monozygotic twins with ASD (MZCo-ASD) and children with typical development (TD). We enrolled 67 subjects aged 2-9 years. Twenty-three pairs of MZCo-ASD and 21 singleton children with TD completed clinical assessments and diffusion tensor imaging (DTI). Graph theory was used to compare the topological properties of the WM network between the two groups, and analyzed their correlations with the severity of clinical symptoms. We found that the global efficiency (Eg) of MZCo-ASD is weaker than that of TD children, while the shortest path length (Lp) of MZCo-ASD is longer than that of TD children, and MZCo-ASD have three unique hubs (the bilateral dorsolateral superior frontal gyrus and right insula). Eg and Lp were both correlated with the repetitive behavior scores of the Autism Diagnostic Interview-Revised (ADI-R) in the MZCo-ASD group, and the nodal efficiency of the dorsal superior frontal gyrus (SFGdor) was correlated with the ADI-R scores of repetitive behaviors. Left SFGdor nodal efficiency was correlated with Repetitive Behavior and Communication, two core symptoms of autism. The results implicated that MZCo-ASD had atypical brain structural network attributes and node distributions. Using MZCo-ASD, we found that the WM topological properties that correlate with the severity of ASD core symptoms were Eg, Lp, and the nodal efficiency of the SFGdor.

Detecting network anomalies using Forman-Ricci curvature and a case study for human brain networks

We analyze networks of functional correlations between brain regions to identify changes in their structure caused by Attention Deficit Hyperactivity Disorder (adhd). We express the task for finding changes as a network anomaly detection problem on temporal networks. We propose the use of a curvature measure based on the Forman–Ricci curvature, which expresses higher-order correlations among two connected nodes. Our theoretical result on comparing this Forman–Ricci curvature with another well-known notion of network curvature, namely the Ollivier–Ricci curvature, lends further justification to the assertions that these two notions of network curvatures are not well correlated and therefore one of these curvature measures cannot be used as an universal substitute for the other measure. Our experimental results indicate nine critical edges whose curvature differs dramatically in brains of adhd patients compared to healthy brains. The importance of these edges is supported by existing neuroscience evidence. We demonstrate that comparative analysis of curvature identifies changes that more traditional approaches, for example analysis of edge weights, would not be able to identify.

Ollivier Persistent Ricci Curvature-Based Machine Learning for the Protein-Ligand Binding Affinity Prediction

Efficient molecular featurization is one of the major issues for machine learning models in drug design. Here, we propose a persistent Ricci curvature (PRC), in particular, Ollivier PRC (OPRC), for the molecular featurization and feature engineering, for the first time. The filtration process proposed in the persistent homology is employed to generate a series of nested molecular graphs. Persistence and variation of Ollivier Ricci curvatures on these nested graphs are defined as OPRC. Moreover, persistent attributes, which are statistical and combinatorial properties of OPRCs during the filtration process, are used as molecular descriptors and further combined with machine learning models, in particular, gradient boosting tree (GBT). Our OPRC-GBT model is used in the prediction of the protein-ligand binding affinity, which is one of the key steps in drug design. Based on three of the most commonly used data sets from the well-established protein-ligand binding databank, that is, PDBbind, we intensively test our model and compare with existing models. It has been found that our model can achieve the state-of-the-art results and has advantages over traditional molecular descriptors.

Robustness of Brain Structural Networks Is Affected in Cognitively Impaired MS Patients

The robustness of brain structural networks, estimated from diffusion MRI data, may be relevant to cognition. We investigate whether measures of network robustness, such as Ollivier-Ricci curvature, can explain cognitive impairment in multiple sclerosis (MS). We assessed whether local (i.e., cortical area) and/or global (i.e., whole brain) robustness, differs between cognitively impaired (MSCI) and non-impaired (MSNI) MS patients. Fifty patients, with Expanded Disability Status Scale mean (m): 3.2, disease duration m: 12 years, and age m: 40 years, were enrolled. Cognitive impairment scores were estimated from the Minimal Assessment of Cognitive Function in Multiple Sclerosis. Images were obtained in a 3T MRI using a diffusion protocol with a 2 min acquisition time. Brain structural networks were created using 333 cortical areas. Local and global robustness was estimated for each individual, and comparisons were performed between MSCI and MSNI patients. 31 MSCI and 10 MSNI patients were included in the analyses. Brain structural network robustness and centrality showed significant correlations with cognitive impairment. Measures of network robustness and centrality identified specific cortical areas relevant to MS-related cognitive impairment. These measures can be obtained on clinical scanners and are succinct yet accurate potential biomarkers of cognitive impairment.

Functional strengthening through synaptic scaling upon connectivity disruption in neuronal cultures

An elusive phenomenon in network neuroscience is the extent of neuronal activity remodeling upon damage. Here, we investigate the action of gradual synaptic blockade on the effective connectivity in cortical networks in vitro. We use two neuronal cultures configurations-one formed by about 130 neuronal aggregates and another one formed by about 600 individual neurons-and monitor their spontaneous activity upon progressive weakening of excitatory connectivity. We report that the effective connectivity in all cultures exhibits a first phase of transient strengthening followed by a second phase of steady deterioration. We quantify these phases by measuring GEFF, the global efficiency in processing network information. We term hyperefficiency the sudden strengthening of GEFF upon network deterioration, which increases by 20-50% depending on culture type. Relying on numerical simulations we reveal the role of synaptic scaling, an activity-dependent mechanism for synaptic plasticity, in counteracting the perturbative action, neatly reproducing the observed hyperefficiency. Our results demonstrate the importance of synaptic scaling as resilience mechanism.

Altered Functional Hubs and Connectivity in Type 2 Diabetes Mellitus Without Mild Cognitive Impairment

Background: Type 2 diabetes mellitus (T2DM)-related cognitive decline is associated with neuroimaging changes. However, only a few studies have focused on early functional alteration in T2DM prior to mild cognitive impairment (MCI). This study aimed to investigate the early changes of global connectivity patterns in T2DM by using a resting-state functional magnetic resonance imaging (rs-fMRI) technique. Methods: Thirty-four T2DM subjects and 38 age-, sex-, and education-matched healthy controls (HCs) underwent rs-fMRI in a 3T MRI scanner. Degree centrality (DC) was used to identify the functional hubs of the whole brain in T2DM without MCI. Then the functional connectivity (FC) between hubs and the rest of the brain was assessed by using the hub-based approach. Results: Compared with HCs, T2DM subjects showed increased DC in the right cerebellum lobules III-V. Hub-based FC analysis found that the right cerebellum lobules III-V of T2DM subjects had increased FC with the right cerebellum crus II and lobule VI, the right temporal inferior/middle gyrus, and the right hippocampus. Conclusions: Increased DC in the right cerebellum regions III-V, as well as increased FC within cerebellar regions and ipsilateral cerebrocerebellar regions, may indicate an important pathophysiological mechanism for compensation in T2DM without MCI.

p53: 800 million years of evolution and 40 years of discovery

The evolutionarily conserved p53 protein and its cellular pathways mediate tumour suppression through an informed, regulated and integrated set of responses to environmental perturbations resulting in either cellular death or the maintenance of cellular homeostasis. The p53 and MDM2 proteins form a central hub in this pathway that receives stressful inputs via MDM2 and respond via p53 by informing and altering a great many other pathways and functions in the cell. The MDM2-p53 hub is one of the hubs most highly connected to other signalling pathways in the cell, and this may be why TP53 is the most commonly mutated gene in human cancers. Initial or truncal TP53 gene mutations (the first mutations in a stem cell) are selected for early in cancer development inectodermal and mesodermal-derived tissue-specific stem and progenitor cells and then, following additional mutations, produce tumours from those tissue types. In endodermal-derived tissue-specific stem or progenitor cells, TP53 mutations are functionally selected as late mutations transitioning the mutated cell into a malignant tumour. The order in which oncogenes or tumour suppressor genes are functionally selected for in a stem cell impacts the timing and development of a tumour.